# Galilean transformations

How do you prove that every galilean transformation of the space $\mathbb R \times \mathbb R^3$ can be written in a unique way as the composition of a rotation, a translation and uniform motion? Thanks!

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Please explain "uniform motion" and clarify whether you are in 4 dimensions or 3 dimensions or 6 dimensions. – Mark Bennet Aug 21 '12 at 18:07
@MarkB: Since the question as written refers to galilean transformations of $\Bbb R\times\Bbb R^3$, doesn't it at least imply very strongly that it is considering one time dimension and three spatial? – MJD Aug 21 '12 at 18:15
@MJD - Thanks for clarification ... – Mark Bennet Aug 21 '12 at 18:24
@Mark Bennet: By uniform motion, I mean something of the form g(t,x) = (t,x+v*t), where v is a three-component velocity and x is a vector in R3. – user34801 Aug 21 '12 at 18:37
@user34801 If you don't get a good answer here after a couple of days, you might try asking on physics.stackexchange.com , where people are more likely to have a clue about galilean transformations. – MJD Aug 21 '12 at 18:51